Adults tickets are $33 for children tickets are $15. A group of 11 people cost $228. Write and solve a system of equations to find how many children and adults are in the group.

Question

Adult tickets to a play cost $33. Tickets for children cost $15. Tickets for a group of 11 people cost a total of $228. Write and solve a system of equations to find how much children and how many adults were in the group.

Answer 1

Hi Sarabi,

Remember that a system of equations involves 2 equations with 2 variables each and we can use one equation to help solve the other equation by simplifying the second to one variable. I know that's a confusing way of explaining how they work, so lets go through this question step by step.

So the information we're given is that there are 11 people total. Let's call

X = number of adults

Y = number of children

so: X + Y = 11

Now let's tackle the price part of the problem. Let's multiply the individual ticket prices by the variable representing the number of people, and add them together to get $228

$33X + $15Y = $228

So now we have a system of equations. So let's use the simpler one to "define" a variable in terms of the other. This just means that we need to solve for one variable in one of the equations. Let's solve for Y in the first equation:

X + Y = 11

Y = 11 - X

Now we know that Y = 11 - X, so let's just plug that in for Y in the second equation:

33X + 15Y = 228

33X + 15(11 - X) = 228

Now we can solve for X:

33X + 15(11-X) = 228

33X + (15 x 11 - 15 x X) = 228

33X + 165 - 15X = 228

33X - 15X = 228 - 165

18X = 63

X = 3.5

And now we can solve for Y by plugging in the value of X into the first equation

X + Y = 11

3.5 + Y = 11

Y = 11 - 3.5

Y = 7.5

So now we're in a difficult position. The math worked out, but we can't have "half of an adult" nor "half of a child" so the answer to this problem does not make logical sense. Sorry about that! Hope this helped!

Answer 2

A=# of adults

C=# kids

A + C = 11

33A +15C = 228

C = 11 - A

33A + 15(!! - A) = 228

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